In the past, there has been a pipe end cutting apparatus disclosed in Japanese Utility Model Publication No. 51-45592. As shown in FIGS. 1 and 2, this pipe end cutting apparatus includes an inner pipe clamping device (102) for holding the end of a pipe (101), a rotary member (104) having a face plate (103) adapted for rotation in a place facing the end of the pipe (101) and mounted on the inner pipe clamping device (102), a plurality of arms (107) each having one end pivotably connected to the rotary member (104) and having the other end formed into a free end and provided with a processing tool (105) and a roller (106) such that the engagement of the processing tools (105) with the end of the pipe (101) also brings the rollers (106) into engagement with the pipe inner surface, and a plurality of elastic members (108) each being adapted to urge the free end of each arm (107) outwardly in the radial direction whereby, as shown in FIG. 3, when the end of the pipe having a radius R is cut by each processing tool (105), provided on the free end of each arm (107), pivotably mounted on a pivot pin (109) of the face plate and having a radius L, the processing tool (105) is positioned at a point A and the angle of inclination between the cutting face of the processing tool (105) and the normal n.sub.1 --n.sub.1 of the pipe is reduced to zero, whereas when the end of a pipe having a radius (R+d) is cut the processing too- (105) is positioned at a point B, and the angle of inclination between the cutting face of the processing tool (105) and the normal n.sub.1 --n.sub.1 of the pipe becomes .alpha..degree..
Now assuming that with a plate having a thickness T, .theta..sub.1 represents the cutting angle when the angle of inclination between the cutting face of the processing tool and the normal n--n of the plate is 0.degree. and .theta..sub.2 and t.sub.2 represent, respectively, the angle of inclination and the thickness in the case where the thickness of the root face is t.sub.1 and the angle of inclination is .alpha..degree. as shown in FIG. 4 the relations of the following equations hold. ##EQU1##
From the equation (1) there holds EQU .theta..sub.2 &gt;.theta..sub.1 ( 3) EQU t.sub.2 =t.sub.1 .multidot.cos .alpha. (4)
From the equation (4) there holds EQU t.sub.2 &lt;t.sub.1 ( 5).
As a result, with the prior art pipe end cutting apparatus, the angle of inclination between the cutting face of the processing tool and the normal of the pipe increases from 0.degree. to .alpha..degree. when there occurs a transition from the condition for cutting the end of the pipe having the radius R to the condition for cutting the end of the pipe having the radius R+d, and thus a comparison between the cutting angle .theta..sub.1 and the root face thickness t.sub.1 obtained when the angle of inclination is 0.degree. and the cutting angle .theta..sub.2, and the root face thickness t.sub.2 obtained when the angle of inclination is .alpha..degree., shows that the value of .theta..sub.2 becomes greater than .theta..sub.1 but the value of t.sub.2 becomes smaller than t.sub.1 as will be seen from the equations (3) and (5).
As described hereinabove, the prior art pipe end cutting apparatus is disadvantageous in that when the pipe diameter changes, the cutting angle and the root face thickness are changed and the cutting accuracy of the pipe end is deteriorated.